spins and topology quantum information...
TRANSCRIPT
Spins and Topology
for
Quantum Information Applications
Alex Matos-AbiagueAssistant Professor
Wayne State University
Department of Physics & Astronomy
…? Q
1. Approaching the limits of conventional electronics
2. Spintronics and spin-based quantum devices
3. Topological matter: Discovering new phases, tailoring new particles
4. Topological quantum computing
5. Summary
Outline
The team
Teaching at WSU:
• Introduction to Modern Physics• Applied Computational Methods• Introduction to Quantum Computing
Dr. Narayan Mohanta(currently at ONL)
Siphiwo Dlamini(PhD student)
Joseph Pakizer(Master student)
Benjamin Hawn(Undergrad student)
Electrical Control of Majorana Bound States Using Magnetic Stripes
N. Mohanta et al. Phys. Rev. Appl. 12, 034048 (2019)
Dr. Mohammad Yahyavi(Postdoc, Jan. 2020)
Detecting Topological Superconductivity by Using a dc-SQUID
(Work in progress)
Signatures of Topological Superconductivity in Josephson junctions
(Work in progress)
Synthetic Spin-Orbit Memristor: Concept Development
(Work in progress)
Fault-Tolerant Topological Quantum Computing with Majorana Bound
States in Josephson-Junction Arrays
Research in Theoretical Condensed Matter:
• Spintronics• Topological Phases of Matter• Solid-State Quantum Computing
Approaching the limits of conventional electronics
1971
2,300
Intel 4004
2015
10,000,000,000
SPARC M7
Evolution of Logic Electronics
1947
1
Physics Nobel Prize 1956 J. Bardeen, W. Brattain, W. Shockley
IBM5150 1981
CPU@ 4.77 MHz
Boeing 757 (1982)Cruising speed: 530 mph
CPU@ 2.5 GHz – 4 GHz
2016 LaptopsMore than 500 times
In less than 1 hour!!!
Approaching the limits of conventional electronics
Apollo Guidance Computer (AGC)64 KB @ 0.043 MHz
IBM System/360 Model 751024 KB & 41 MB/s
2018Smartphones
1969Apollo 11 Mission
Any smartphone nowadays has much larger memory capacity and is much more powerful than the computers used in the Apollo 11 mission altogether
Approaching the limits of conventional electronics
Current challenges:
• Increasing heat & power consumption.
• Increasing cost (we run out of money before we run out of physics)
• Ultimate physical limit to miniaturization: We will have to change the rules of the game
Approaching the limits of conventional electronics
Ways out:
• Improve performance by optimizing the device architecture (short lasting solution).
• Revolutionize the “hardware” by implementing an alternative to conventional electronics. → Spintronics (longer lasting solution)
• Revolutionize both “hardware” and “software” by changing the conceptual basis on which classical computing operates. → Quantum computing(ultimate solution)
Approaching the limits of conventional electronics
= S|e|mc
Magnetic moment
e charge - classical property
S spin - quantum property ( )
“1” (): spin up state
“0” (): spin down state
+
-
SPIN Magnetism
Spintronics and spin-based quantum devices
Why not using the spin degree of freedom of the carriers?
• Low energy consumption
• Non volatility
• High integration between logic and memory
• High speed
Natural advantages of using the spin
I. Žutić, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)
J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Žutić, Acta Phys. Slovaca 57, 565 (2007)
Spintronics (spin electronics)
Spintronics and spin-based quantum devices
Giant Magnetoresistance (GMR) and Tunneling Magnetoresistance (TMR)
GMR spin valve
Albert Fert Peter Grünberg
The Nobel Prize in Physics, 2007
• In 1997 GMR was in magnetic hard drives
• Stuart Parkin, Millenium Technology Prize 2014
GMR discovered in 198815 GN and 30 GN (25.7 Gb/in2) and 48 GH (21.7 Gb/in2)
AFC MEDIA
(FIRST INDUSTRY PRODUCT)
GLASS MEDIA SUBSTRATE
RAMP LOAD/UNLOAD
ADVANCED GMR HEADS
15 GBytes/DISK
2 DISK DRIVE CAPACITY
30 Gbytes
25.7 Gbits/In2
TMR spin valve
FM1 FM2
RP
I FM1 FM2
RAP
I
FM1 FM2
RP
NM FM1 FM2
RAP
NM
Low resistance (1) High resistance (0)
In 2004 TMR started to replace GMR
Spintronics and spin-based quantum devices
Spin solar cells
J. Sinova et al. Nat. Mater. 11, 368 (2012)
Spin lasers
Spin LEDs
T. Taniyama et al. Asia Mater. 3, 65 (2011)
Spin batteries
P. N. Hai et al. Nature 458, 489 (2009)
Spin photodiodes
R. Jansen et al. Nat. Mater. 12, 779 (2013)
TMR sensors & memories
MRAM
Spin Transistor
S. Datta et al. Appl. Phys. Lett. 56, 665 (1998)
Spintronics and spin-based quantum devices
Ultimately, there are certain problems that, for practical purposes, can’t be solved in a classical computer. The need of quantum computers in the future seems inevitable.
Spintronics and spin-based quantum devices
Prime factorization problem
• Every integer number can be broken down into prime number factors, e.g. 15 = 5x3, 12 =3x2x2, etc.
• Given the prime factors, finding the number is an easy problem, one just need to multiply the factors.
• Given the number, finding the prime factors is a hard problem. The time a classical computer needs to find the prime factors of the number 𝑁 scales exponentially with ln 𝑁 . However, the time it takes a quantum computer to solve the problem is polynomial in ln(𝑁). If 𝑁 is sufficiently large the prime factorization becomes intractable for a classical computer, while a quantum computer could still quickly find the prime factors.
Spintronics and spin-based quantum devices
Classical bits
or
Quantum bits (qubits)
𝑐1 0 + 𝑐2|1⟩
𝑃0 = 𝑐12
𝑃1 = 𝑐22
𝑛 qubits encode as much information as 2𝑛 bits!
A register with 𝑛 qubits may contain more integer numbers (2500) than the number of atoms in the known universe (∼ 2330)!
Unlike a classical bit, the state of a single qubit is not 0 or 1 but a superposition of 0 and 1 (i.e. 0 and 1 at the same time). Therefore, a 𝑛-qubit quantum computer can do operations involving the equivalent of 2𝑛 bits in parallel (i.e, at once). This quantum parallelism allows a quantum computer to solve certain class of problems much faster than a classical computer. Quantum computers can also solve certain problems that are completely intractable with a classical computer
Example: Finding a secret number
Spintronics and spin-based quantum devices
Quantum computing: State of the art
Google 53-qubit quantum computer solved a problem in 200 seconds that the most powerful supercomputer in the world (IBM’s Summit) will need 10,000 years (according to Google) or 2.5 days (according to IBM) to solve it
Spintronics and spin-based quantum devices
Companies Developing Quantum Computing Devices
• IBM• Google• IonQ• Quantum Circuits, Inc (QCI)• Rigetti• Intel• Microsoft
IBM Q Experience provide open access to some of their quantum computers
Research division on topological quantum computing but no actual quantum computer yet.Partnering with IonQ and QCI will provide access to quantum computers through Microsoft Azure cloud service
Remarks:
• Magnetic textures can lead to quasiparticle confinement
• Magnetic textures produce synthetic spin-orbit coupling
Requirements for magnetic textures to be used in quantum device applications:
• Inhomogeneity at the nanoscale
• Tunability at the nanoscale
N. Mohanta, T. Zhou, J.-W. Xu, J. E. Han, A. D. Kent, J. Shabani, I. Žutić, and A. Matos-Abiague. Phys. Rev. Appl. 12, 034048 (2019)A. Matos-Abiague, J. Shabani, A. D. Kent, G. L. Fatin, B. Scharf, I. Žutić, Solid State Commun. 262, 1 (2017)G. L. Fatin, A. Matos-Abiague, B. Scharf, and I. Žutić, Phys. Rev. Lett. 117, 077002 (2016)
General idea: Use the interaction between spin and magnetic field texture to control the motion and state of electrons
Spintronics and spin-based quantum devices
Spintronics to the rescue
• Use fringe fields of spin valve arrays• Modulate the texture by spin valve switching
Tesla
0.08
-0.08
0
0.04
-0.04
𝐵𝑧
𝐵𝑥
𝐵𝑧
𝐵𝑥
OFF ON
Spintronics and spin-based quantum devices
Probability density (normalized to its maximum) of ground state for a 5-nanopilar array on a (Cd,Mn)Te two-dimensional electron gas (2DEG)
2DEG
I
1-nanopilar cell
Spintronics and spin-based quantum devices
Quantum Computing with Quantum Dots
𝒒𝟏 𝒒𝟐
Spintronics and spin-based quantum devices
Synthetic Spin-Orbit Memristor: A Theoretical Proposal
A. Sengupta et al., Appl. Phys. Express 11, 030101 (2018)
Artificial Neural Networks for AI
Spintronics and spin-based quantum devices
Topology is a branch of mathematics concerned with spatial properties preserved under continuous deformation. It is a characterization of geometric objects on the basis of continuous transformations rather than on their specific shapes or form.
Example: A coffee mug and a donut are topologically equivalent
Example: Three topologically non-equivalent objects
Topological matter: Discovering new phases, tailoring new particles
Topological classes are characterized by topological invariants (topological numbers)
Gauss-Bonnet Theorem Number of holes as a topological invariant
𝑛 = 0 𝑛 = 1 𝑛 = 2 𝑛 = 3
Topological matter: Discovering new phases, tailoring new particles
No. of holes
0
1
2
3
... …
D. J. Thouless F. D. M. Haldane J. M. Kosterlitz
Nobel Prize 2016
Topological Phase Transitions
Example of topological changes of a material
Topological matter: Discovering new phases, tailoring new particles
Integer Quantum Hall EffectNobel Prize 1985
Klaus von KlitzingAccuracy of 1 in a billion!!!
Topological matter: Discovering new phases, tailoring new particles
1. Dissipationless edge (surface states)
2. Spin-momentum locking
3. Massless Dirac fermions (Cond. Mat. meets Special & General Relativity)
Magnetic control of carriers motion
Electric generation of spin polarization
Electric generation of spin currents
Experimental signatures of topological transition in the presence of a magnetic field:
B Scharf, A Matos-Abiague, J Fabian, Physical Review B 86 (7), 075418B Scharf, A Matos-Abiague, I Žutić, J Fabian, Physical Review B 91 (23), 235433
Topological matter: Discovering new phases, tailoring new particles
Topological Superconductors
• New properties • Not found in nature but can be
artificially engineered• Support Majorana bound states
B
Research goals:
• Explore new phases of matter in heterostructures with proximity effects
• Identify new phenomena and their signatures
• Investigate potential applications
semiconductor wiresuperconductor
Topological matter: Discovering new phases, tailoring new particles
Review Article: Proximitized Materials, I. Zutic, A. Matos-Abiague et al., Materials Today 22, 85 (2019)
• Discover of new particles
• Need of ever higher energies(Currently in the order of TeV)
• Use collisions to break down interactions and decompose particles into smaller ones
Particle Physics
• Discover of new quasiparticles
• Need very low energy excitations(Currently from meV to eV)
• Integrate various interactions to build new quasiparticles
Condensed Matter Physics
Topological matter: Discovering new phases, tailoring new particles
quasiparticle
particle
• Skyrmions (as magnetic textures)
• Dirac Fermions (graphene, topological insulators)
• Weyl Fermions (Weyl semimetals)
• Composite Fermions (Fractional Quantum Hall systems)
• Anyons (excitations in Fractional Quantum Hall systems )
• Majorana Modes (Topological superconductors)
• Parafermions (Fractional Quantum Hall systems & Topological superconductors)
• …
Exotic Quasiparticles in Condensed Matter Physics
?
Topological matter: Discovering new phases, tailoring new particles
1. Chargeless
2. Spinless
3. Massless• Zero energy pairs of degenerate states
• Protected by energy gap
Majorana Bound States:
E. Majorana, Il Nuovo Cimento 14, 171 (1937)
Majorana fermions are their own antiparticles
→ ො𝛾† = ො𝛾
Majorana: Real Field
Dirac: Complex Field
Majoranas in Kitaev’s chain
A. Y. Kitaev, Phys. Usp. 44, 131 (2001)
Topological quantum computing
Conventional Qubits vs Topological Qubits
Conventional Qubits:
• Information is stored locally and qubits are fragile
• Local perturbations can cause errors
• Large amount of error corrections needed
Topological Qubits:
• Information is stored non-locally
• Qubits are protected against local perturbations
• Small or no error corrections needed
Topological quantum computing
Braiding Operations for Fault-Tolerant Topological Quantum Computing
f i
f
i
Topological quantum computing
A. Matos-Abiague et al., Solid State Commun. 262, 1 (2017)
G. L Fatin, A. Matos-Abiague et al. Phys. Rev. Lett. 117, 077002 (2016)
(b) W. G. Wang et al., Sci. Rep 3, 1948 (2013)
(d) A. D. Kent et al., Nat. Nanotech. 10, 187 (2015)
MRAM-like architecture for fault-tolerant topological quantum computing
Topological quantum computing
Goal: To develop theoretical prototypes of wireless quantum circuits by using topological superconductors
Remarks:• The effective topological wires are reconfigurable and
programmable, and so is the circuit• The circuit is non-volatile• If coupled to an artificial neural network of magnetic nanopilars
the circuit can become intelligent
A 𝑛-terminal quantum device can support 2𝑛 different connectivity patterns
Topological quantum computing
How to induce a topological phase transition from the trivial superconducting to the topological superconducting state?
How to measure such a transition?
Topological Superconductivity in Josephson Junctions
Phase Signature of Topological Transition in
Josephson Junctions
W, Mayer et al. arXiv:1906.01179 (2019)
S N S
In the topological superconducting phase, two Majorana states form at the ends of the N region
Topological quantum computing
• First experimental realization of self-tuned phase transition into the topological superconducting state
• First clear signatures of topological superconductivity by two different measurements
Closing and re-opening of the superconducting gap
Phase Signature of Topological Transition in Josephson Junctions. W, Mayer et al. arXiv:1906.01179 (2019)
Theory developed @ WSU Experiment@ NYU
Self-tuned phase jump
Topological quantum computing
https://phys.org/news/2019-08-scientists-state.html
https://scitechdaily.com/scientific-breakthrough-new-state-of-matter-discovered/https://bigthink.com/surprising-science/physicists-find-state-supercharge-technologyhttps://nyunews.com/news/2019/09/03/nyu-professor-state-of-matter/
Further theoretical developments @ WSU
• Joseph Pakizer (Master)Topological superconductivity in proximitizedtransition metal dichalcogenide Josephson junctions (APS March meeting, 2020)
• Benjamin Hawn (Undergrad)Detecting topological superconductivity by using a dc-SQUID (APS March meeting, 2020)
Topological quantum computing
Available Financial Support
Engineering Topological States Using Electrically-Tunable Magnetic Chains
Nanoelectronics with Proximitized Materials
WSU, NYU, SUNY Buffalo
WSU, SUNY Buffalo
• Spintronics uses the spin degree of freedom in addition to charge to provide faster and
less energy consuming devices for both memory and logic. Typical examples are spin
valves, which applications range from sensors to magnetic random access memories.
• The coupling of spin to a tunable magnetic texture produced by an array of magnetic
tunnel junction nanopilars provides new possibilities for controlling electronic states.
• Topological phases (e.g., topological insulators and superconductors) are protected
against local perturbations and can therefore encode quantum information immune to
the undesired effects of the environment. In particular, Majorana modes are very
promising for the implementation of fault-tolerant topological quantum computing.
• Reconfigurable magnetic textures could be used for building a versatile architecture for
topological quantum computing and for the design of programmable, intelligent
quantum circuits.
Prof. Alex Matos AbiagueEmail: [email protected]: 391
Summary
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